Respuesta :
Question:
Denzel earned money after school. He put 1/2 of this month's earnings into savings. He took the rest to spend at the amusement park. He spent 1/5 of this amount on popcorn and 3/4 of it on rides. What fraction of his earnings did he take to the park but not spend on rides or popcorn.
Answer:
[tex]\frac{1}{40}[/tex] fraction of money not spend in amusement park
Solution:
Let "x" be the total earnings
He put 1/2 of this month's earnings into savings
[tex]\text{ savings} = \frac{1}{2} \text{ of } x[/tex]
[tex]\text{ savings} = \frac{1}{2}x = \frac{x}{2}[/tex]
He took the rest to spend at the amusement park
[tex]\text{ Remaining amount }= x - \frac{x}{2}\\\\\text{ Remaining amount } = \frac{2x - x}{2} = \frac{x}{2}[/tex]
He spent 1/5 of this amount on popcorn and 3/4 of it on rides
[tex]\text{ Amount spend on popcorn } = \frac{1}{5} \times \frac{x}{2} = \frac{x}{10}[/tex]
[tex]\text{ amount spend on rides } = \frac{3}{4} \times \frac{x}{2} = \frac{3x}{8}[/tex]
So the fraction of money not spend in amusement park is:
⇒ Remaining amount - (Amount spend on popcorn + amount spend on rides)
[tex]\rightarrow \frac{x}{2} - (\frac{x}{10} + \frac{3x}{8})\\\\\rightarrow \frac{x}{2} - \frac{38x}{80}\\\\\rightarrow \frac{2x}{80} = \frac{x}{40}[/tex]
Thus [tex]\frac{1}{40}[/tex] fraction of money not spend in amusement park
